On Using the Shapley Value for Anomaly Localization: A Statistical Investigation

--Recent publications have suggested using the Shapley value for anomaly localization for sensor data systems. Using a reasonable mathematical anomaly model for full control, experiments indicate that using a single fixed term in the Shapley value calculation achieves a lower complexity anomaly localization test, with the same probability of error, as a test using the Shapley value for all cases tested. A proof demonstrates these conclusions must be true for all independent observation cases. For dependent observation cases, no proof is available. The incorporation of sensors into many systems provides important advantages [1]-[7]. Sensor data is highly vulnerable to cyber attacks and cyber attacks on sensor data can cause tremendous damage.